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fa-inbox fa-fw post-meta-icon"></i><a class="post-meta-categories" href="/categories/%E7%AE%97%E6%B3%95%E7%BB%83%E4%B9%A0/">算法练习</a></span></div><div class="meta-secondline"><span class="post-meta-separator">|</span><span class="post-meta-wordcount"><i class="far fa-file-word fa-fw post-meta-icon"></i><span class="post-meta-label">字数总计:</span><span class="word-count">904</span><span class="post-meta-separator">|</span><i class="far fa-clock fa-fw post-meta-icon"></i><span class="post-meta-label">阅读时长:</span><span>4分钟</span></span><span class="post-meta-separator">|</span><span class="post-meta-pv-cv" id="" data-flag-title="小于n的最大数"><i class="far fa-eye fa-fw post-meta-icon"></i><span class="post-meta-label">阅读量:</span><span id="busuanzi_value_page_pv"><i class="fa-solid fa-spinner fa-spin"></i></span></span></div></div></div></header><main class="layout" id="content-inner"><div id="post"><article class="post-content" id="article-container"><h1 id="题目描述"><a href="#题目描述" class="headerlink" title="题目描述"></a>题目描述</h1><p>数组nums中给定可以使用的1~9的数，返回由数组nums中的元素组成的小于n的最大数。</p>
<p>示例 1：</p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入：nums = &#123;1, 2, 9, 4&#125;，n = 2533</span><br><span class="line">输出：2499</span><br></pre></td></tr></table></figure>

<p>示例 2：</p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入：nums = &#123;1, 2, 5, 4&#125;，n = 2543</span><br><span class="line">输出：2542</span><br></pre></td></tr></table></figure>

<p>示例 3：</p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入：nums = &#123;1, 2, 5, 4&#125;，n = 2541</span><br><span class="line">输出：2525</span><br></pre></td></tr></table></figure>

<p>示例 4：</p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入：nums = &#123;1, 2, 9, 4&#125;，n = 2111</span><br><span class="line">输出：1999</span><br></pre></td></tr></table></figure>

<p>示例 5：</p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入：nums = &#123;5, 9&#125;，n = 5555</span><br><span class="line">输出：999</span><br></pre></td></tr></table></figure>

<p>示例 6：</p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入：nums = &#123;5, 9&#125;，n = 3</span><br><span class="line">输出：-1</span><br></pre></td></tr></table></figure>

<h1 id="我的解法"><a href="#我的解法" class="headerlink" title="我的解法"></a>我的解法</h1><h2 id="思路"><a href="#思路" class="headerlink" title="思路"></a>思路</h2><ol>
<li>对每一位先尝试使用相同数字</li>
<li>如果没有相同数字，判断是否存在比当前数字更小的数字，如果有，则选择更小数字中的最大数，剩余的数字用最大数字</li>
<li>如果没有，向前查找前一个数字有没有更小的数字</li>
<li>直到回溯到第一个数字，就用位数更少但全部都是最大的数</li>
</ol>
<h2 id="代码"><a href="#代码" class="headerlink" title="代码"></a>代码</h2><p>在实际代码编写中我们添加一个标志末尾字符，当遍历到此字符时必定会向前查找，统一因缺少数字与所有数字都包含的情况，例如：</p>
<ol>
<li>缺少数字</li>
</ol>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入：nums = &#123;1, 2, 9, 4&#125;，n = 2533</span><br><span class="line">输出：2499</span><br></pre></td></tr></table></figure>

<p>2533遍历到第一个3时，因为nums数组中不存在3，因此需要向前一位查找更小的数字</p>
<ol start="2">
<li>所有数字都包含</li>
</ol>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">输入：nums = &#123;1, 2, 9, 4&#125;，n = 2111</span><br><span class="line">输出：1999</span><br></pre></td></tr></table></figure>

<p>2111遍历完毕，所有的数字都包含，最后结果为2111，因此需要再向前一位查找更小的数字</p>
<p>添加一个标志末尾字符的目的就是统一以上两种情况，避免重复编码，值得注意的是添加的标志字符的ASCII码值应小于’0’，必须使set.lower(num)返回为null。</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">class</span> <span class="title class_">Solution</span> &#123;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">public</span> <span class="type">int</span> <span class="title function_">getMaxNumBelowN</span><span class="params">(<span class="type">int</span>[] nums, <span class="type">int</span> n)</span> &#123;</span><br><span class="line">        TreeSet&lt;Integer&gt; set = <span class="keyword">new</span> <span class="title class_">TreeSet</span>&lt;&gt;();</span><br><span class="line">        Arrays.stream(nums).forEach(set::add);</span><br><span class="line">        <span class="type">StringBuilder</span> <span class="variable">result</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">StringBuilder</span>();</span><br><span class="line">        <span class="type">int</span> <span class="variable">max</span> <span class="operator">=</span> Arrays.stream(nums).max().getAsInt();</span><br><span class="line">        <span class="type">StringBuilder</span> <span class="variable">s</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">StringBuilder</span>(String.valueOf(n)).append(<span class="string">&#x27;!&#x27;</span>);</span><br><span class="line">        <span class="keyword">for</span> (<span class="type">int</span> <span class="variable">i</span> <span class="operator">=</span> <span class="number">0</span>; i &lt; s.length(); i++) &#123;</span><br><span class="line">            <span class="type">int</span> <span class="variable">num1</span> <span class="operator">=</span> s.charAt(i) - <span class="string">&#x27;0&#x27;</span>;</span><br><span class="line">            result.append(s.charAt(i));</span><br><span class="line">            <span class="keyword">if</span> (!set.contains(num1)) &#123;</span><br><span class="line">                <span class="comment">// 从当前位置向前查找</span></span><br><span class="line">                <span class="keyword">for</span> (<span class="type">int</span> <span class="variable">j</span> <span class="operator">=</span> result.length() - <span class="number">1</span>; j &gt;= <span class="number">0</span>; j--) &#123;</span><br><span class="line">                    <span class="type">int</span> <span class="variable">num</span> <span class="operator">=</span> result.charAt(j) - <span class="string">&#x27;0&#x27;</span>;</span><br><span class="line">                    result.deleteCharAt(j);</span><br><span class="line">                    <span class="type">Integer</span> <span class="variable">lower</span> <span class="operator">=</span> set.lower(num);</span><br><span class="line">                    <span class="keyword">if</span> (lower != <span class="literal">null</span>) &#123;</span><br><span class="line">                        result.append(lower);</span><br><span class="line">                        <span class="keyword">while</span> (result.length() &lt; s.length() - <span class="number">1</span>) &#123;</span><br><span class="line">                            result.append(max);</span><br><span class="line">                        &#125;</span><br><span class="line">                        <span class="keyword">return</span> Integer.parseInt(result.toString());</span><br><span class="line">                    &#125;</span><br><span class="line">                &#125;</span><br><span class="line">                <span class="comment">// 不存在小于n的最大数</span></span><br><span class="line">                <span class="type">int</span> <span class="variable">length</span> <span class="operator">=</span> s.length() - <span class="number">2</span>;</span><br><span class="line">                <span class="keyword">if</span> (length == <span class="number">0</span>) &#123;</span><br><span class="line">                    <span class="keyword">return</span> -<span class="number">1</span>;</span><br><span class="line">                &#125;</span><br><span class="line">                <span class="comment">// 向前未找到小于n的最大数</span></span><br><span class="line">                <span class="keyword">return</span> Integer.parseInt(String.valueOf(max).repeat(length));</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">return</span> -<span class="number">1</span>;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<h2 id="测试"><a href="#测试" class="headerlink" title="测试"></a>测试</h2><p>添加测试用例：</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">class</span> <span class="title class_">Test</span> &#123;</span><br><span class="line">    <span class="type">int</span>[] nums;</span><br><span class="line">    <span class="type">int</span> n;</span><br><span class="line">    <span class="type">int</span> expect;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">public</span> <span class="title function_">Test</span><span class="params">(<span class="type">int</span>[] nums, <span class="type">int</span> n, <span class="type">int</span> expect)</span> &#123;</span><br><span class="line">        <span class="built_in">this</span>.nums = nums;</span><br><span class="line">        <span class="built_in">this</span>.n = n;</span><br><span class="line">        <span class="built_in">this</span>.expect = expect;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="keyword">public</span> <span class="keyword">class</span> <span class="title class_">Main</span> &#123;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title function_">main</span><span class="params">(String[] args)</span> &#123;</span><br><span class="line">        <span class="type">Solution</span> <span class="variable">solution</span> <span class="operator">=</span> <span class="keyword">new</span> <span class="title class_">Solution</span>();</span><br><span class="line">        Test[] testList = <span class="keyword">new</span> <span class="title class_">Test</span>[]&#123;</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">1</span>, <span class="number">2</span>, <span class="number">9</span>, <span class="number">4</span>&#125;, <span class="number">2533</span>, <span class="number">2499</span>),</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">1</span>, <span class="number">2</span>, <span class="number">5</span>, <span class="number">4</span>&#125;, <span class="number">2543</span>, <span class="number">2542</span>),</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">1</span>, <span class="number">2</span>, <span class="number">5</span>, <span class="number">4</span>&#125;, <span class="number">2541</span>, <span class="number">2525</span>),</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">1</span>, <span class="number">2</span>, <span class="number">9</span>, <span class="number">4</span>&#125;, <span class="number">2111</span>, <span class="number">1999</span>),</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">1</span>, <span class="number">2</span>, <span class="number">9</span>, <span class="number">4</span>&#125;, <span class="number">1111</span>, <span class="number">999</span>),</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">5</span>, <span class="number">9</span>&#125;, <span class="number">5555</span>, <span class="number">999</span>),</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">5</span>, <span class="number">9</span>&#125;, <span class="number">33</span>, <span class="number">9</span>),</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">5</span>, <span class="number">9</span>&#125;, <span class="number">3</span>, -<span class="number">1</span>),</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">5</span>, <span class="number">9</span>, <span class="number">7</span>&#125;, <span class="number">9</span>, <span class="number">7</span>),</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">6</span>, <span class="number">7</span>, <span class="number">8</span>&#125;, <span class="number">1200</span>, <span class="number">888</span>),</span><br><span class="line">                <span class="keyword">new</span> <span class="title class_">Test</span>(<span class="keyword">new</span> <span class="title class_">int</span>[]&#123;<span class="number">1</span>, <span class="number">2</span>, <span class="number">4</span>, <span class="number">9</span>&#125;, <span class="number">4921</span>, <span class="number">4919</span>),</span><br><span class="line">        &#125;;</span><br><span class="line">        <span class="keyword">for</span> (Test test : testList) &#123;</span><br><span class="line">            <span class="type">int</span> <span class="variable">maxNumBelowN</span> <span class="operator">=</span> solution.getMaxNumBelowN(test.nums, test.n);</span><br><span class="line">            System.out.println((maxNumBelowN == test.expect) + <span class="string">&quot;------&gt;&quot;</span> + maxNumBelowN);</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<p>运行启动类，查看控制台：</p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line">true------&gt;2542</span><br><span class="line">true------&gt;2525</span><br><span class="line">true------&gt;1999</span><br><span class="line">true------&gt;999</span><br><span class="line">true------&gt;999</span><br><span class="line">true------&gt;9</span><br><span class="line">true------&gt;-1</span><br><span class="line">true------&gt;7</span><br><span class="line">true------&gt;888</span><br><span class="line">true------&gt;4919</span><br></pre></td></tr></table></figure>
</article><div class="post-copyright"><div class="post-copyright__author"><span class="post-copyright-meta">文章作者: </span><span class="post-copyright-info"><a href>狼族少年、血狼</a></span></div><div class="post-copyright__type"><span class="post-copyright-meta">文章链接: </span><span class="post-copyright-info"><a href="https://geekwolfman.github.io/2023/04/11/%E5%B0%8F%E4%BA%8En%E7%9A%84%E6%9C%80%E5%A4%A7%E6%95%B0.html">https://geekwolfman.github.io/2023/04/11/小于n的最大数.html</a></span></div><div class="post-copyright__notice"><span class="post-copyright-meta">版权声明: </span><span class="post-copyright-info">本博客所有文章除特别声明外，均采用 <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/" target="_blank">CC BY-NC-SA 4.0</a> 许可协议。转载请注明来自 <a href="https://geekwolfman.github.io" target="_blank">狼族少年、血狼</a>！</span></div></div><div class="tag_share"><div class="post-meta__tag-list"><a class="post-meta__tags" href="/tags/%E7%AE%97%E6%B3%95%E9%A2%98/">算法题</a></div><div class="post_share"><div 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class="toc-number">1.</span> <span class="toc-text">题目描述</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E6%88%91%E7%9A%84%E8%A7%A3%E6%B3%95"><span class="toc-number">2.</span> <span class="toc-text">我的解法</span></a><ol class="toc-child"><li class="toc-item toc-level-2"><a class="toc-link" href="#%E6%80%9D%E8%B7%AF"><span class="toc-number">2.1.</span> <span class="toc-text">思路</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E4%BB%A3%E7%A0%81"><span class="toc-number">2.2.</span> <span class="toc-text">代码</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E6%B5%8B%E8%AF%95"><span class="toc-number">2.3.</span> <span class="toc-text">测试</span></a></li></ol></li></ol></div></div></div></div></main><footer id="footer"><div id="footer-wrap"><div class="copyright">&copy;2020 - 2023 By 狼族少年、血狼</div><div class="framework-info"><span>框架 </span><a target="_blank" rel="noopener" href="https://hexo.io">Hexo</a><span 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